I would say go to a store that sells the tape that is used for lathe turning.
It is pressure sensitive so you have to use force to press it down.... It peels off of without a lot effort which will not happen if you happen to get a paper backed one.... I got a roll this paper stuff by mistake one time.... I still have it but never use it because of the effort it takes to peel off.
No not get double stick foam tape..... often about 1/16" thick, you will spend more time getting the mess off then woodworking.
Carpet tape I've tried but didn't like, it never seem to hold as well as I like but that is maybe just me??????
The last roll I got was about $10 for a 1" wide..... sorry I don't recall the length..... This tape does hold very well and you don't need to use as much of it as would with say carpet tape.
Ed